Suppose also that in this economy of inflation, researchers are concerned that consumers are spending less. In previous years, the mean monthly spending was $525. Provide a separate analysis to determine at the 0.10 significance level, if the mean amount spent per month significantly decreased this year. This is a one-sample mean test. Please provide: (8 points)1) The null and alternative hypotheses indicating whether it is a one or two-sided test.2) Use Data analysis and descriptive statistics to obtain the necessary summary statistics to perform this analysis. Clean up the output and copy and paste the clean output below.3) Calculate the appropriate Test Statistic showing your work which should include the point estimate and its standard error. Either copy and paste your calculations in Excel or show your hand calculations.4) Compare either the p-value to the level of significance OR your test statistic to the proper critical value and make the necessary conclusion.5) a concluding statement reporting the results of the test and the proper decisions that follow from the analysis in the context of the data.
Question
Suppose also that in this economy of inflation, researchers are concerned that consumers are spending less. In previous years, the mean monthly spending was $525. Provide a separate analysis to determine at the 0.10 significance level, if the mean amount spent per month significantly decreased this year. This is a one-sample mean test. Please provide: (8 points)1) The null and alternative hypotheses indicating whether it is a one or two-sided test.2) Use Data analysis and descriptive statistics to obtain the necessary summary statistics to perform this analysis. Clean up the output and copy and paste the clean output below.3) Calculate the appropriate Test Statistic showing your work which should include the point estimate and its standard error. Either copy and paste your calculations in Excel or show your hand calculations.4) Compare either the p-value to the level of significance OR your test statistic to the proper critical value and make the necessary conclusion.5) a concluding statement reporting the results of the test and the proper decisions that follow from the analysis in the context of the data.
Solution
- The null and alternative hypotheses:
The null hypothesis (H0): The mean monthly spending has not decreased this year. (μ = 525) This is a one-sided test because we are only interested in whether the mean monthly spending has decreased.
- Use Data analysis and descriptive statistics:
Without the actual data, I can't provide the descriptive statistics. However, you would typically use software like Excel or SPSS to calculate the mean, standard deviation, and sample size of your data.
- Calculate the appropriate Test Statistic:
The test statistic for a one-sample mean test is calculated as (sample mean - population mean) / (standard deviation / sqrt(sample size)). Again, without the actual data, I can't calculate this for you.
- Compare either the p-value to the level of significance OR your test statistic to the proper critical value:
If the p-value is less than the level of significance (0.10 in this case), we reject the null hypothesis. If the test statistic is less than the critical value (which would be negative for a one-sided test where we're looking for a decrease), we also reject the null hypothesis.
- A concluding statement:
Without the actual calculations, I can't provide a specific conclusion. However, the conclusion would state whether or not there is sufficient evidence to conclude that the mean monthly spending has decreased this year, based on the p-value or test statistic. If we reject the null hypothesis, we would conclude that the mean monthly spending has significantly decreased. If we fail to reject the null hypothesis, we would conclude that there is not enough evidence to say the mean monthly spending has decreased.
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